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We study the asymptotic behavior of ruin probabilities, as the initial reserve goes to infinity, for a reserve process model where claims arrive according to a renewal process, while between the claim times the process has the dynamics of…

Probability · Mathematics 2023-02-24 Ying He , Konstantin Borovkov

The discrete time risk model with two seasons and dependent claims is considered. An algorithm is created for computing the values of the ultimate ruin probability. Theoretical results are illustrated with numerical examples.

Probability · Mathematics 2020-01-13 Olga Navickienė , Jonas Sprindys , Jonas Šiaulys

Inspired by the double-debt problem in Japan where the mortgagor has to pay the remaining loan even if their house was destroyed by a catastrophic event, we model the lender's cash flow, by an exponential functional of a renewal-reward…

Probability · Mathematics 2020-09-24 J. Akahori , C. Constantinescu , Y. Imamura , Hh. Pham

We study the ruin problem over a risk process described by a discrete-time Markov model. In contrast to previous studies that focused on the asymptotic behaviour of ruin probabilities for large values of the initial capital, we provide a…

Risk Management · Quantitative Finance 2013-08-26 Ilya Tkachev , Alessandro Abate

Consider a multi-dimensional Brownian motion which models the surplus processes of multiple lines of business of an insurance company. Our main result gives exact asymptotics for the cumulative Parisian ruin probability as the initial…

Probability · Mathematics 2020-04-28 Lanpeng Ji

We consider a generalization of the classical risk model when the premium intensity depends on the current surplus of an insurance company. All surplus is invested in the risky asset, the price of which follows a geometric Brownian motion.…

Probability · Mathematics 2014-03-28 Yuliya Mishura , Mykola Perestyuk , Olena Ragulina

This paper develops asymptotics and approximations for ruin probabilities in a multivariate risk setting. We consider a model in which the individual reserve processes are driven by a common Markovian environmental process. We subsequently…

Probability · Mathematics 2018-12-24 G. A. Delsing , M. R. H. Mandjes , P. J. C. Spreij , E. M. M. Winands

We study a dynamic model of a non-life insurance portfolio. The foundation of the model is a compound Poisson process that represents the claims side of the insurer. To introduce clusters of claims appearing, e.g. with catastrophic events,…

Risk Management · Quantitative Finance 2026-03-03 Jonathan Klinge , Maren Diane Schmeck

We consider a two-dimensional ruin problem where the surplus process of business lines is modelled by a two-dimensional correlated Brownian motion with drift. We study the ruin function $P(u)$ for the component-wise ruin (that is both…

Probability · Mathematics 2019-08-07 Krzysztof Debicki , Lanpeng Ji , Tomasz Rolski

The ruin probability in the classical Brownian risk model can be explicitly calculated for both finite and infinite-time horizon. This is not the case for the simultaneous ruin probability in two-dimensional Brownian risk model. Resorting…

Probability · Mathematics 2018-11-13 Krzysztof Dȩbicki , Enkelejd Hashorva , Zbigniew Michna

We investigate an insurance risk model that consists of two reserves which receive income at fixed rates. Claims are being requested at random epochs from each reserve and the interclaim times are generally distributed. The two reserves are…

Probability · Mathematics 2015-08-05 E. S. Badila , O. J. Boxma , J. A. C. Resing

We consider a modification of the dividend maximization problem from ruin theory. Based on a classical risk process we maximize the difference of expected cumulated discounted dividends and total expected discounted additional funding…

Portfolio Management · Quantitative Finance 2019-01-21 Josef Anton Strini , Stefan Thonhauser

This paper considers the ruin problem with random premiums, whose densities have rational Laplace transforms, and investments in a risky asset whose price follows a geometric Brownian motion. The asymptotic behavior of the ruin probability…

Probability · Mathematics 2025-08-12 Viktor Antipov

The claim arrival process to an insurance company is modeled by a compound Poisson process whose intensity and/or jump size distribution changes at an unobservable time with a known distribution. It is in the insurance company's interest to…

Optimization and Control · Mathematics 2008-12-10 Erhan Bayraktar , H. Vincent Poor

We consider continuous time risk processes in which the claim sizes are dependent and non-identically distributed phase-type distributions. The class of distributions we propose is easy to characterize and allows to incorporate the…

Probability · Mathematics 2023-07-28 Oscar Peralta , Matthieu Simon

We consider an insurance company in the case when the premium rate is a bounded non-negative random function $c_\zs{t}$ and the capital of the insurance company is invested in a risky asset whose price follows a geometric Brownian motion…

Risk Management · Quantitative Finance 2010-11-08 Serguei Pergamenchtchikov , Zeitouny Omar

We consider the valuation problem of an (insurance) company under partial information. Therefore we use the concept of maximizing discounted future dividend payments. The firm value process is described by a diffusion model with constant…

Mathematical Finance · Quantitative Finance 2016-02-16 Gunther Leobacher , Michaela Szölgyenyi , Stefan Thonhauser

In this note we find a formula for the supremum distribution of spectrally positive or negative L\'evy processes with a broken linear drift. This gives formulas for ruin probabilities in the case when two insurance companies (or two…

Probability · Mathematics 2019-01-01 Zbigniew Michna

Important models in insurance, for example the Carm{\'e}r--Lundberg theory and the Sparre Andersen model, essentially rely on the Poisson process. The process is used to model arrival times of insurance claims. This paper extends the…

Statistics Theory · Mathematics 2019-04-16 Arun Kumar , Nikolai Leonenko , Alois Pichler

In the extended gambler's ruin problem we can move one step forward or backward (classical gambler's ruin problem), we can stay where we are for a time unit (delayed action) or there can be absorption in the current state (game is…

Probability · Mathematics 2023-03-28 Theo van Uem